Subordinated discrete semigroups of operators

Details Subordinated discrete semigroups of operators Subordinated discrete semigroups of operators

2008-01-29

arxiv.org/abs/0801.4557v1

Mathematics

Functional Analysis

28 pages

Scientific paper

Given a power-bounded linear operator T in a Banach space and a probability F on the non-negative integers, one can form a `subordinated' operator S = \sum_k F(k) T^k. We obtain asymptotic properties of the subordinated discrete semigroup (S^n: n=1,2,...) under certain conditions on F. In particular, we study probabilities F with the property that S satisfies the Ritt resolvent condition whenever T is power-bounded. Examples and counterexamples of this property are discussed. The hypothesis of power-boundedness of T can sometimes be replaced by the weaker Kreiss resolvent condition.

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